Brushless DC motor

ABSTRACT

A bridge ( 8 ) in conformity with a tooth opening angle of the stator ( 1 ) is provided between a permanent magnet ( 5 ) and a permanent magnet ( 5 ) in a rotor ( 4 ), so that a magnetic flux for a reluctance torque is made to pass an inner side of the permanent magnet ( 5 ). An opening angle of each of ribs ( 7 ) on both sides of the permanent magnet ( 5 ) is set to be equal to or smaller than the teeth interval opening angle and equal to or larger than a half thereof. Thereby, reluctance of the rib ( 7 ) against a magnetic flux in a circumferential direction is increased and leakage of the magnetic flux of the permanent magnet ( 5 ) is prevented.

The present Application is a Divisional Application of U.S. patentapplication Ser. No. 10/233,656, filed on Sep. 4, 2002 now U.S. Pat. No.6,867,526.

BACKGROUND OF THE INVENTION

The present invention relates to a brushless DC motor having a permanentmagnet at a rotor thereof. Further in details, the invention relates toa brushless DC motor utilizing a reluctance torque for effectivelyutilizing the reluctance torque while preventing a cogging torque fromincreasing as less as possible.

Conventionally, there is a brushless DC motor of this kind utilizing areluctance torque having a constitution shown by, for example, FIG. 47.That is, according to a rotor 101 of a brushless DC motor of thedrawing, a permanent magnet 102 is arranged on an inner side of an outerperiphery to some degree. Therefore, a magnetic region 103 is presentbetween the outer periphery of the rotor 101 and the permanent magnet102. In driving the motor, as shown by an arrow mark of “q axis” in thedrawing, a magnetic flux produced by a stator passes through themagnetic region 103 of the rotor 101. The magnetic flux generates areluctance torque. Meanwhile, a magnetic flux produced by the permanentmagnet 102 also passes through the magnetic region 103 (“d axis” in thedrawing). The magnetic flux generates a magnet torque. Further, in thedrawing a stator coil and a lower half of the motor are omitted (similarto other drawing of the same kind).

However, according to the above-described conventional brushless DCmotor utilizing the reluctance torque, there poses a problem explainedbelow. That is, according to the brushless DC motor, as mentioned above,a magnetic path is commonly used by the magnetic flux produced by thepermanent magnet 102 and the magnetic flux produced by the stator(magnetic region 103). The following unpreferable various phenomena arebrought about thereby. Further, the phenomena are similar also in abrushless DC motor of a type providing a plurality of rows of permanentmagnets at respective magnetic poles of a rotor as shown by FIG. 48.

First, it is pointed out that the magnetic region 103 is significantlymagnetized. Therefore, the magnetic region 103 is liable to fall intomagnetic saturation. When the magnetic saturation is brought about, thetorque of the motor is not proportional to magnetic excitation of astator coil and is not increased considerably. Therefore, the energyefficiency is poor. Therefore, a characteristic of the motor isdeteriorated and vibration or noise by harmonics are increased by thatamount.

Further, since the magnetic path is commonly used by the two magneticfluxes, when some measure is taken with regard to one of the magnetictorque and the reluctance torque, an influence is effected on the otherthereby. For example, when there is taken a measure of reducing acogging torque component of the magnet torque, a magnitude of thereluctance torque or a torque waveform is influenced thereby. Or, whenthe reluctance torque is intended to be increased, a magnitude of themagnet torque or the torque waveform is conversely influenced thereby.Therefore, design of the motor is very difficult.

Further, there also poses a problem that a magnetic flux densitydistribution becomes uniform at a gap between the rotor and the stator.An explanation will be given of the problem in reference to a graph ofFIG. 49. The abscissa of the graph designates an angle around an axis ofthe brushless DC motor of FIG. 47. A section A of the angle designatesan angular range in correspondence with the single permanent magnet 102in the rotor 101. Meanwhile, the ordinate designates a magnetic fluxdensity. Further, a broken line designates a magnetic flux densitydistribution in no load time (when the stator is not excited). A boldline designates a magnetic flux density distribution in load time (whenthe stator is excited). According to the graph, in no load time (brokenline), the magnetic flux distribution is substantially uniform in thesection A. In contrast thereto, in load time (bold line), the magneticflux distribution is deviated even in the section A. The deviation iscaused by influence of the magnetic flux of the q axis. That is, becauseeven in the angular range in correspondence with the single permanentmagnet 102, at a right half thereof and a left half thereof, a tone ofthem, the magnetic flux is strengthened and at other thereof, themagnetic flux is weakened. The more strengthened the excitation currentof the stator in order to achieve a strong torque, the more significantis a warp of the magnetic flux distribution.

Further, according to the brushless DC motor of FIG. 47, a leakagemagnetic flux flowing from one permanent magnet to a contiguouspermanent magnet without interlinking with the stator coil, is so largethat the leakage magnetic flux cannot be disregarded. This signifiesthat magnetic force of the permanent magnet cannot be made full use asthe magnet torque.

According to a conventional brushless DC motor, a torque function ispromoted by increasing an amount of using magnets in a rotor as large aspossible. For example, according to a rotor shown in FIG. 50, aneffective magnetic pole opening angle of a magnet is set to be near toalmost 180° in electric angle. Thereby, the magnetic flux is increasedand a torque function is ensured by a magnet torque.

However, according to the above-described conventional technology, thereposes the following problem. That is, the higher the torque of thebrushless DC motor is intended to achieve, the larger the number ofmagnets are needed. The fact constitutes a factor of cost. Further, whenthe motor is of a type in which a magnetic member of a rotor is presenton an outer side of a magnet as shown by FIG. 50 for utilizing areluctance torque, there also poses the following problem. That is, amagnetic path is commonly used by a magnetic flux related to a magnettorque and a magnetic flux related to a reluctance torque. Therefore,the magnetic member at the commonly used portion is liable to fall tomagnetic saturation. Due to the fact, there is a case in which a torquein proportion to excitation is not achieved. Further, a magnetic fluxdistribution in an air gap between a rotor and a stator, becomessignificantly nonuniform due to the magnetic flux related to thereluctance torque. The fact deteriorates properties of the motor andcauses vibration or noise by harmonics.

SUMMARY OF THE INVENTION

The invention has been carried out in order to resolve theabove-described problem of the conventional brush DC motor utilizing thereluctance torque. That is, it is an object of the invention to separatea magnetic path by a magnetic flux of a magnetic torque and a magneticflux of a reluctance torque to thereby exclude adverse influenceproduced by mutual influence of the magnetic fluxes. Further, it is anobject of invention to exclude leakage of a magnetic flux of a permanentmagnet as less as possible to make full use of the magnetic flux as amagnet torque.

Another object of the invention is to provide a brushless DC motorcapable of achieving a necessary torque without using so many number ofmagnets and alleviating both of the problem of magnetic saturation andthe problem of nonuniformity of magnetic flux density.

In order to solve the aforesaid object, the invention is characterizedby having the following arrangement.

(1) A brushless DC motor comprising

a rotor attached with permanent magnets at equal pitches in acircumferential direction, the rotor including,

-   -   a bridge connecting a portion on an inner side of the permanent        magnet and a portion on an outer side thereof, and    -   a rib disposed between an end portion in the circumferential        direction of an effective magnetic pole opening angle of the        permanent magnet and a front end of the bridge along a side edge        thereof; and

a stator including a plurality of teeth aligned at equal pitches in thecircumferential direction, and a plurality of slots defined betweenadjacent teeth,

wherein an opening angle θr produced by viewing the bridge from a centerof the rotor, is equal to or larger than a tooth width opening angle θthin the stator and equal to or smaller than an angle constituting anunexcited section of the stator in driving the motor.

(2) The blushless DC motor according to (1), wherein the bridge openingangle θr is set to an angle determined by the following equation:θr=(θtp×n)+θth

where

θtp: a slot pitch angle

θth: the tooth width opening angle

n: 0 or a natural number.

(3) The brushless DC motor according to (1), wherein a rib opening angleθd produced by viewing the rib from the center of the rotor, falls in arange specified by the following equation:0.5×θop≦θd≦θop

where θop: an opening angle between the adjacent teeth in the stator.

(4) A brushless DC motor comprising

a rotor attached with permanent magnets at equal pitches in acircumferential direction, the rotor including,

-   -   a bridge connecting a portion on an inner side of the permanent        magnet and a portion on an outer side thereof, and    -   a rib disposed between an end portion in the circumferential        direction of an effective magnetic pole opening angle of the        permanent magnet and a front end of the bridge along a side edge        thereof; and

a stator including a plurality of teeth aligned at equal pitches in thecircumferential direction, and a plurality of slots defined betweenadjacent teeth,

wherein a rib opening angle θd produced by viewing the rib from a centerof the rotor, falls in a range specified by the following equation:0.5×θop≦θd≦θop

where θop: an opening angle between the adjacent teeth in the stator.

(5) A brushless DC motor comprising:

a rotor including a magnet; and

a stator arranged with a plurality of slots at equal pitches in acircumferential direction;

wherein a width in a diameter direction of a rib portion of the rotordoes not exceed a value given by the following Equation:$\sqrt{\frac{R \times {Wm}}{{Bz}/{Bm}} \times {Lr}}$where,

-   R: a rate of a leakage magnetic flux at a rib portion to a magnetic    flux progressing from the magnet to the stator-   Wm: an effective magnetic pole width in circumferential direction-   Bz: a saturation magnetic flux density of a magnetic member of the    rotor-   Bm: a magnetic flux density of the rib portion of the rotor in a    radial direction of the rotor-   Lr: a length in the circumferential direction of the rib portion.    (6) The brushless DC motor according to (5),

wherein a contribution of a magnet torque to a total torque is largerthan a contribution of a reluctance torque to the total torque.

(7) The brushless DC motor according to (5),

wherein a value of Bz/Bm falls in a range of 1.8 through 4.4.

(8) A brushless DC motor comprising:

a rotor having a magnet; and

a stator arranged with a plurality of slots at equal pitches in acircumferential direction;

wherein a width in a diameter direction of a rib portion of the rotordoes not exceed a value given by the following Equation:$\frac{Q \times {Wb}}{{Bz}/{Bb}} \times \frac{( {{Lr} + {Wm}} )}{Lb}$where,

-   Q: a rate of a leakage magnetic flux at the rib portion to a    magnetic flux passing from a tooth of the stator to a bridge of the    rotor-   Wb: a width in a circumferential direction of the bridge of the    rotor-   Wm: an effective magnetic pole width in circumferential direction-   Bz: a saturation magnetic flux density of a magnetic member of the    rotor-   Bb: a magnetic flux density of a bridge of the rotor in driving the    motor-   Lr: a length in the circumferential direction of the rib portion-   Lb: a length in a diameter direction of the bridge.    (9) The brushless DC motor according to (8),

wherein a contribution of a magnet torque to a total torque is largerthan a contribution of a reluctance torque to the total torque.

(10) The brushless DC motor according to (8),

wherein a value of Bz/Bb falls in a range of 1.8 through 4.4.

(11) A structure of a brushless DC motor comprising:

a rotor having a magnet; and

a stator arranged with a plurality of slots at equal pitches in acircumferential direction;

wherein a width in a diameter direction of a rib portion of the rotordoes not exceed a smaller one of a value given by the following Equation1: $\begin{matrix}\sqrt{\frac{R \times {Wm}}{{Bz}/{Bm}} \times {Lr}} & {{Equation}\mspace{14mu} 1}\end{matrix}$and a value given by the following Equation 2: $\begin{matrix}{\frac{Q \times {Wb}}{{Bz}/{Bb}} \times \frac{( {{Lr} + {Wm}} )}{Lb}} & {{Equation}\mspace{20mu} 2}\end{matrix}$where,

-   R: a rate of a leakage magnetic flux at a rib portion to a magnetic    flux progressing from the magnet to the stator-   Q: a rate of a leakage magnetic flux at the rib portion to a    magnetic flux passing from a tooth of the stator to a bridge of the    rotor-   Wm: an effective magnetic pole width in circumferential direction-   Bz: a saturation magnetic flux density of a magnetic member of the    rotor-   Bm: a magnetic flux density of the rib portion of the rotor in a    radial direction of the rotor-   Bb: a magnetic flux density of a bridge of the rotor in driving the    motor-   Lr: a length in the circumferential direction of the rib portion-   Wb: a width in the circumferential direction of the bridge of the    rotor-   Lb: a length in a diameter direction of the bridge.    (12) The structure of a brushless DC motor according to (11)

wherein a value Bz/Bm and a value Bz/Bb fall in a range of 1.8 through4.4.

(13) A brushless DC motor utilizing a reluctance torque comprising:

a rotor including magnets,

wherein an effective magnetic pole opening angle in an air gap of therotor falls in a range specified by two conditions of an upper limit of173° and a lower limit of 127° in electric angles.

(14) The brushless DC motor according to (13), wherein the upper limitis 161° and a lower limit is 139° in electric angles.

(15) The brushless DC motor according to (13), wherein

the rotor includes a bridge for connecting an inner periphery and anouter periphery of the magnet by a magnetic member at a position otherthan the effective magnetic pole opening angle in the rotor, and

an opening angle in an electric angle of the bridge is not smaller than83.3% of a complementary angle in an electric angle of the effectivemagnetic pole opening angle in the rotor.

(16) The brushless DC motor according to (15), wherein

the motor is driven by an excitation current having a phase angleadvanced relative to a phase of an induced voltage, and

an advancing angle of the phase of the current relative to the phase ofthe induced voltage falls a range in which a center of the range isdefined by a half of the opening angle in the electric angle of thebridge and a width of the range is defined by an opening angle in anelectric angle of a width of a tooth constituting an excitation centerof a reluctance torque.

(17) A method of driving a brushless DC motor, in which the brushless DCmotor includes a rotor having a magnet, an effective magnetic poleopening angle in an air gap of the rotor falls in a range prescribed bytwo conditions of an upper limit of 173° and a lower limit of 127° inelectric angles, the brushless DC motor includes a bridge for connectingan inner periphery and an outer periphery of the magnet by a magneticmember at a portion other than the effective magnetic pole opening anglein the rotor, and an opening angle in an electric angle of the bridge isnot smaller than 83.3% of a complementary angle in an electric angle ofthe effective magnetic pole opening angle in the rotor, the methodcomprising the steps of:

using an excitation current having a phase angle advanced relative to aphase of an induced voltage; and

setting an advancing angle of a phase of the current relative to thephase of the induced voltage in a range in which a center of the rangeis defined by a half of the opening angle in the electric angle of thebridge and a width of the range is defined by an opening angle in anelectric angle of a width of a tooth constituting an excitation centerof a reluctance torque.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a view showing a structure of a brushless DC motor accordingto a first embodiment.

FIG. 2 is a view showing signs of angles of respective portions of thebrushless DC motor of FIG. 1.

FIG. 3 is a view for explaining windings of the brushless DC motor ofFIG. 1.

FIG. 4 illustrates diagrams for explaining an excitation situation inthe brushless DC motor of FIG. 1.

FIG. 5 is a view showing a structure of a brushless DC motor accordingto a modified example of the first embodiment.

FIG. 6 illustrates views showing variations of shapes of front ends ofteeth in a brushless DC motor.

FIG. 7 is a view showing a variation of a shape of a front end of atooth in a brushless DC motor.

FIG. 8 is a view for explaining magnetic paths in the brushless DC motorof FIG. 1.

FIG. 9 is a view showing a relationship between magnetic poles of arotor and teeth of a stator in the brushless DC motor of FIG. 1 bylinear development.

FIG. 10 is a view showing a relationship between the magnetic poles ofthe rotor and the teeth of the stator in the brushless DC motor of FIG.1 by linear development.

FIG. 11 is a view showing a relationship between the magnetic poles ofthe rotor and the teeth of the stator in the brushless DC motor of FIG.1 by linear development.

FIG. 12 is a graph showing a situation of torques generated by abrushless DC motor according to the first embodiment.

FIG. 13 is a view showing a relationship between magnetic poles of arotor and teeth of a stator in a brushless DC motor according to amodified example by linear development.

FIG. 14 is a view showing a relationship between magnetic poles of arotor and teeth of a stator in a brushless DC motor according to amodified example by linear development.

FIG. 15 is a view showing a structure of a rotor in a brushless DC motoraccording to a modified example.

FIG. 16 is an outline constitution view of a brushless DC motoraccording to a second embodiment.

FIG. 17 is a view showing a rotor in FIG. 16.

FIG. 18 is a linear development view showing a flow of a magnetic fluxof a magnet of the rotor.

FIG. 19 is a graph showing a magnetic flux density of a magnetic fluxrelated to a magnet torque.

FIG. 20 is a linear development view showing a flow of a magnetic fluxinterlinking with the rotor from a stator.

FIG. 21 is a graph showing a difference between inductance Lq andinductance Ld.

FIG. 22 is a graph showing a magnetization curve of a representativemagnetic member.

FIG. 23 is a graph showing a torque of the brushless DC motor accordingto the second embodiment.

FIG. 24 is a graph showing a torque of a brushless DC motor in which amagnetic torque is dominant.

FIG. 25 is a graph showing a torque of a brushless DC motor in which areluctance torque is dominant.

FIG. 26 is a view showing a rotor in which a magnet is attached todeviate.

FIG. 27 is a view showing a rotor having a magnet in a linear shape.

FIG. 28 is a view showing a structure of a brushless DC motor accordingto a third embodiment.

FIG. 29 is a view for explaining angles of respective portions of arotor in FIG. 28.

FIG. 30 is a view showing a situation of interlinking magnetic fluxes inthe rotor in FIG. 28.

FIG. 31 is a graph showing inductance when an effective magnetic poleopening angle is changed in the rotor in FIG. 28.

FIG. 32 is a graph showing a torque when the effective magnetic poleopening angle is changed in the brushless DC motor of FIG. 28.

FIG. 33 is a waveform diagram showing an advancing phase of excitationcurrent relative to induced voltage.

FIG. 34 is a vector diagram showing the advancing phase of theexcitation current.

FIG. 35 is a vector diagram showing the advancing phase of theexcitation current.

FIG. 36 is a view for explaining a situation of interlinking a magneticflux by the excitation current having the advancing phase with a bridgeof a rotor.

FIG. 37 illustrates views showing a relationship between a situation ofaligning a bridge and a tooth and a reluctance torque.

FIG. 38 is a graph showing the relationship between the situation ofaligning the bridge and the tooth and the reluctance torque.

FIG. 39 is a view for explaining a situation of interlinking themagnetic flux by the excitation current having the advancing phase withthe bridge of the rotor.

FIG. 40 is a view for explaining a situation of interlinking themagnetic flux by the excitation current having the advancing phase withthe bridge of the rotor.

FIG. 41 is a view showing a shape of a front end of a tooth of a stator.

FIG. 42 is a view showing a situation in corresponding with a situationof FIG. 36 in a conventional brushless DC motor.

FIG. 43 is a graph showing a situation of generating a torque in thecase of only a magnet torque for comparison.

FIG. 44 is a graph showing a situation of compensating for a valley of amagnet torque by a reluctance torque.

FIG. 45 is a view showing a rotor of a brushless DC motor according to afirst modified example of the third embodiment.

FIG. 46 is a view showing a rotor of a brushless DC motor according to asecond modified example of the third embodiment.

FIG. 47 is a view showing an example of a structure of a conventionalbrushless DC motor.

FIG. 48 is a view showing other example of a structure of a conventionalbrushless DC motor.

FIG. 49 is a graph showing a magnetic flux density distribution of a gapin a brushless DC motor.

FIG. 50 is a view showing an example of a structure of a conventionalbrushless DC motor.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS First Embodiment

A detailed explanation will be given of embodiments embodying theinvention in reference to the attached drawings as follows. Theembodiment embodies the invention as a brushless DC motor constituted bya stator having 12 slots and a rotor having 4 poles. According to theembodiment, an angular range of an opening angle used in each ofportions of the stator and the rotor, is defined by a portion facing anair gap (inner periphery in the stator, outer periphery in the rotor).

A brushless DC motor according to the embodiment is constituted by astructure as shown in FIG. 1. A stator 1 of the brushless DC motor isprovided with 12 pieces of teeth 2. A front end of the respective tooth2 is formed with a tip 3. Meanwhile, a rotor 4 is provided with 4 piecesof permanent magnets 5. The respective permanent magnet 5 is formed by ashape of a so-to-speak substantially circular arc along an outerperiphery of the rotor 4. A respective magnet attaching hole 6 in therotor 4 is formed to be longer than the permanent magnet 5 in acircumferential direction. Further, the respective permanent magnet 5 isattached at substantially a center of the respective magnet attachinghole 6 in the circumferential direction. Therefore, there are gaps atboth ends of the respective permanent magnets 5. The respective magnetattaching hole 6 is formed to be extremely proximate to the outerperiphery of the rotor 4. Therefore, a magnetic member on an outer sideof the respective magnet attaching hole 6 is extremely slender. In thespecification, a portion of the magnetic member on the outer side of therespective magnet attaching hole 6 on an outer side of the gap at eachof the both end portions of the permanent magnet 5 in thecircumferential direction, is referred to as a rib 7. There is present abridge 8 for connecting a central portion of the rotor 4 and the rib 7between the magnet attaching hole 6 and the magnet attaching hole 6.

An explanation will be given of names of angles of respective portionsin the brushless DC motor of FIG. 1 in reference to FIG. 2. That is, apitch of arranging the permanent magnet 5 in the rotor 4, is referred toas a magnetic pole pitch angle θp. An angular range occupied by thepermanent magnet 5 in view from the center of the rotor 4, is referredto as an effective magnetic pole opening angle θm. An angular rangeoccupied by the rib 7 in view from the center of the rotor 4, isreferred to as a rib opening angle θd. An angular range occupied by thebridge 8 in view from the center of the rotor 4, is referred to as abridge opening angle θr1.

Further, a pitch of arranging a slot in the stator 1, is referred to asa slot pitch angle θtp. An angular range occupied by the tooth 2 of thestator 1 in view from the center of the rotor 4, is referred to as thetooth opening angle θth. Although in FIG. 2, an angular range of aportion of the tooth 2 which does not include the tip 3, is shown as thetooth opening angle θth, as mentioned later in reference to FIG. 5, anangular range including the tips 3 on both sides can also be defined asthe tooth opening angle θth. An angular range occupied by an intervalbetween the teeth 2 of the stator 1 in view from the center of the rotor4, is referred to as a teeth interval opening angle θop. Although inFIG. 2, the interval between the teeth 2 per se excluding the tips 3, isshown as the teeth interval opening angle θop, as mentioned later inreference to FIG. 5, an opening angle of an opening between the tip 3and the tip 3 (slot opening angle), may be defined as the teeth intervalopening angle θop. Further, an angular range occupied by the teeth 2(here, 2 pieces thereof as mentioned later) simultaneously excited andan opening therebetween in the stator 1, is referred to as an effectiveexcitation opening angle θe and the angle constituting an unexcitedsection of the stator is shown as θue in FIG. 2. The unexcited sectionof the stator θue corresponds to the angle that is obtained when theeffective excitation opening angle θe is subtracted from the magneticpole pitch θp. Similar to the tooth opening angle θth, although in FIG.2, the range of a portion of the teeth 2 which does not include the tip3, is shown as an effective excitation opening angle θe, as mentionedlater in reference to FIG. 5, an angular range including the tip 3 onboth sides can also be defined as an effective excitation opening angleθe.

Next, an explanation will be given of windings in the brushless DC motorin reference to FIG. 3. The windings adopt a winding method referred toas abbreviated winding and a number of phases is 3. Numbers of 1 through12 in FIG. 3 are numbers of slots in the stator 1. That is, a wire of Uphase winds 3 pieces of the teeth 2 from 1-th slot to 4-th slot,further, winds 3 pieces of the teeth 2 from 7-th slot to 10-th slot andreaches a neutral point. A wire of V phase winds 3 pieces of the teeth 2from 3-th slot to 6-th slot, further, winds 3 pieces of the teeth 2 from9-th slot to 12-th slot and reaches the neutral point. A wire of W phasewinds 3 pieces of the teeth 2 from 5-th slot to 8-th slot, further,winds 3 pieces of the teeth 2 from 11-th slot to 2-th slot and reachesthe neutral point. That is, the three phases are wound while beingshifted from each other by 2 slot pitch. Further, respective closed loopexcites 3 pieces of the teeth 2. According to the brushless DC motor, 6pieces of the teeth 2 correspond to an electric angle of 360° andtherefore, one closed loop ranges an electric angle of 180°. Further,the shift between phases corresponds to an electric angle of 120°.

Here, assume that electricity is conducted from U phase to V phase.Then, at the teeth 2 between 3-th slot and 4-th slot, excitation of twophases are canceled by each other and therefore, the teeth 2 are notexcited in a synthesized state. The same goes with the teeth 2 between9-th slot and 10-th slot. Further, also between 6-th slot and 7-th slotand between the 12-th slot and 1-th slot, the teeth 2 at the positionsare not excited. Therefore, the teeth 2 are excited effectively at 4locations from 1-th slot to 3-th slot, from 4-th slot to 6-th slot, from7-th slot to 9-th slot and from 10-th slot to 12-th slot respectively byan amount of 2 slot pitches (electric angle of 120°). In the previousexplanation of the effective excitation opening angle θe, 2 pieces ofthe teeth 2 are simultaneously excited from such reason. Naturally, adirection of excitation is alternating. That is, when electricity isconducted from U phase to V phase, there is brought about an excitedsituation as shown by an upper stage of FIG. 4. A lower stage of FIG. 4shows a case of conducting electricity from U phase to W phase. The samegoes with a case of conducting electricity to other phases. Further, anumeral in the abscissa of FIG. 4 designates a slot number shown in FIG.3. The ordinate indicates an intensity of excitation generated atrespective slot.

Further, in the case of conducting electricity in sine wave, more orless excitation appears also in the unexcited teeth in FIG. 4. However,main excited magnetic poles are invariably constituted by the amount of2 teeth and the way of specifying the effective excitation opening angleθe is not influenced thereby. In the following explanation, also inconsideration of such a case, “nonexcitation” is defined by including ofweakly excited teeth relative to the main excited poles.

Referring back to FIG. 1 and FIG. 2, the bridge opening angle θr1(corresponding to “bridge opening angle θr” in claims) of the rotor 4 isset to be equal to the opening angle θth viewing one tooth 2 in thestator 1 (portion excluding the chip 3). The reason is that a magneticflux produced by exciting the stator coil is drawn to a portion of therotor 4 on an inner side of the permanent magnet 5. A description willbe given later of the details.

Further, as shown by FIG. 5, the bridge opening angle (corresponding to“bridge opening angle θr in claims) of the rotor may be set to anopening angle θr2 including the tips 3 on the both sides of the tooth 2.Such a setting is particularly effective when the teeth 2 and the tip 3constitute a smoothly connected shape as shown by FIG. 6 or when the tip3 is formed thickly in the radius direction. Because in such a case, amagnetic flux produced by the stator coil is diffused in thecircumferential direction by the tip 3. Therefore, in such a case, alsothe effective excitation opening angle θe is to be set to an openingangle including the tips 3 at the both ends.

Meanwhile, when the tip 3 is thin in the radius direction and there is aclear notch between the tip 3 and the tooth 2 as shown by FIG. 7, it iseffective to set the bridge opening angle θr1 as shown by FIG. 1 andFIG. 2. Because in such a case, a magnetic flux produced by exciting thestator coil is not so much diffused at the chip 3. Therefore, in such acase, also the effective excitation opening angle θe is to be set to theopening angle which does not include the tip 3 at the both ends.

Referring back to FIG. 1 and FIG. 2 again, the rib opening angle θd ofthe rotor 4 is set to be equal to or smaller than the teeth intervalopening angle θop and equal to or larger than a half thereof of thestator 1. Further, the rib 7 is extremely slender in the radiusdirection. A description will be given later of reason therefor.

According to the brushless DC motor having the above-describedconstitution, magnetic paths are formed as shown by FIG. 8. That is, themagnetic flux by the permanent magnet 5 (“d axis” in the drawing)traverses the extremely slender magnetic member on the outerside of thepermanent magnet 5 in the rotor 4 and comes out to the gap between therotor 4 and the stator 1. Further, the magnetic flux progresses to thetooth 2 of the stator 1 and is interlinked with the coil. The magneticflux carries burden of the magnet torque of the brushless DC motor.Meanwhile, when the teeth 2 (tees within the effective excitationopening angle θe) of the stator 1 and the bridges 8 of the rotor 4 arealigned as shown by FIG. 8, the magnetic flux (“q axis” in the drawing)generated by the coil of the stator 1 passes the bridge 8 and entersfrom the permanent magnet 5 to the inner side and returns to the stator1 from other bridge 8. The magnetic flux carries burden of thereluctance torque of the brushless DC motor. In this way, the brushlessDC motor of the embodiment is of a type of positively utilizing thereluctance torque.

Therefore, the magnetic paths of the two magnetic fluxes are separate.Therefore, there is almost no interference between the two magneticfluxes and the magnetic member of the rotor 4 does not fall intomagnetic saturation. Therefore, the energy efficiency is high. Further,the width of the bridge 8 is set in conformity with the tooth 2 (referto the above-described explanation of the bridge opening angle θr1) andtherefore, there is not a portion at which a sectional area of themagnetic flux path of the q axis is narrowed at inside of the rotor 4.This signifies that reluctance to the magnetic flux of the q axis issmall. Therefore, large reluctance torque is provided. Further, when thetooth 2 at a position attached with an arrow mark of “d axis” in FIG. 8,is an excitation pole, the magnetic flux needs to detour to the bridge 8by passing the rib 7 of the rotor 4 in the circumferential direction. Asa result, such a magnetic flux is extremely small.

Successively, an explanation will be given of a leakage magnetic flux inthe magnetic flux produced by the permanent magnet 5 in the brushless DCmotor. First, an explanation will be given of a situation when thebridges 8 of the rotor 4 are aligned with the teeth 2 of the stator 1(FIG. 9). The magnetic flux generated by the permanent magnet 5 passesthe teeth 2 of the stator 1 via the gap and is interlinked with thestator coil as shown by arrow marks φm1 and φm2 in FIG. 9. Thereby, themagnetic torque is generated. Here, a portion of the magnetic fluxgenerated by the permanent magnet 5 progresses to contiguous permanentmagnet 5 by way of the rib 7, a front of the bridge 8 and the rib 7 asshown by an arrow mark φs1 in FIG. 9. Further, as shown by an arrow markφr1, there also is a component thereof which progresses to contiguouspermanent magnet 5 by way of the rib 7, the gap, the front end of theteeth 2, the gap, and the rib 7.

The magnetic fluxes of the arrow marks φs1 and φr1 progress directly tothe contiguous permanent magnet 5 without interlinking with the statorcoil and therefore, the magnetic fluxes do not contribute to the magnettorque. Therefore, these are leakage magnetic fluxes. However, both ofthe magnetic fluxes need to pass the ribs 7 in the circumferentialdirection. The rib 7 is extremely slender in the radius direction asdescribed above and therefore, reluctance thereof to the magnetic fluxesis very large. Therefore, the leakage fluxes are actually extremelylittle.

Next, an explanation will be given of a situation when the bridge 8 ofthe rotor 4 is aligned with the slot opening of the stator 1 (FIG. 10).Also in this case, a large portion of the magnetic flux generated by thepermanent magnet 5 passes the tooth 2 of the stator 1 and is interlinkedwith the stator coil (arrow marks φm3, φm4). This is the componentcontributing to the magnet torque. Further, there are leakage magneticfluxes which do not contribute to the magnet torque as shown by arrowmarks φs2 and φr2. The former progresses to contiguous permanent magnet5 by way of the rib 7, the front end of the bridge 8 and the rib 7. Thelatter progresses to contiguous permanent magnet 5 by way of the rib 7,the gap, the front end of the tooth 2, the slot opening, the front endof the tooth 2, the gap and the rib 7. However, the leakage magneticfluxes are axially extremely little. The reason is similar to that inthe explanation in reference to FIG. 9. Particularly, the leakagemagnetic flux of the arrow mark φr2 is very little. Because thereluctance is larger by an amount of passing the throttle opening.

In this way, according to the brushless DC motor, in the magnetic fluxgenerated by the permanent magnet 5, the leakage magnetic flux componentwhich does not contribute to the magnet torque is extremely little. Thissignifies that the magnetic force of the permanent magnet 5 caneffectively be utilized as torque. Further, that the leakage magneticflux component is very little, signifies that a variation width by arotational position of the rotor 4 (difference between the case of FIG.9 and the case of FIG. 10) is also little. This signifies that thecogging torque produced by the variation of the leakage magnetic fluxamount is small. Therefore, a consideration may be given to only avariation by the rotational position of the rotor 4 with regard to themagnetic flux interlinking with the stator coil from the permanentmagnet 5 as the cogging torque of the magnetic torque in the brushlessDC motor.

Further, an explanation will be given of influence of the rib openingangle θd effected on large or small of the leakage magnetic flux inreference to FIG. 11. FIG. 11 shows a situation when the bridges 8 arealigned with the teeth 2 of the stator 1. Under the situation, asdescribed above, a large portion of the magnetic flux from the permanentmagnet 5 is interlinked with the stator coil (arrow mark φm), however,there is present the magnetic flux which is not interlinked with thestator coil although the amount is very small (arrow mark φr). In thiscase, when the rib opening angle θd is smaller than a half of the teethinterval opening angle θop of the stator 1, the magnetic flux φr whichis not interlinked with the stator coil is increased. Because themagnetic flux φr flows by constituting a closed circuit by end portionsof contiguous ones of the permanent magnets 5 of the rotor 4 in thecircumferential direction and the tooth 2 right thereabove.

Therefore, the lib opening angle θd needs to be equal to or larger thanthe half of the teeth interval opening angle θop. When the rib openingangle θd is made to be equal to or larger than the half of the teethinterval opening angle θop, the magnetic flux φr which is notinterlinked with the stator coil becomes negligibly small. Thereby, theleakage magnetic flux amount can be much reduced.

When the rib opening angle θd is conversely made larger than the teethinterval opening angle θop, a total amount of the magnetic flux of thepermanent magnet 5 is reduced on one hand and the function of thebrushless DC motor is deteriorated. Further, on the other hand, thebridge opening angle θr1 is reduced and reluctance torque cannoteffectively be utilized. At any rate, this is not preferable in view ofthe function of the motor. From the above-described, the rib openingangle θd is set to fall in a range shown below.0.5×θop≦θd≦θopAs a result, according to the brushless DC motor of the embodiment, itis most advantageous in view of the function of the motor that theeffective magnetic pole opening angle θm of the rotor 4 and theeffective excitation opening angle θe of the stator 1 are substantiallyequal to each other. Hence, according to the embodiment, assume that thetwo opening angles are set in this way.

Further, FIG. 11 shows an example of the case of the motor (FIG. 2) inwhich the bridge opening angle θr of the rotor 4 is set to the openingangle θr1 of the tooth 2 of the stator 1 excluding the tip 3. In thecase of the motor in which the bridge opening angle θr of the rotor 4 isset to the opening angle θr2 including the tips 3 on the both sides ofthe tooth 2, the above-described equation is applied after the teethinterval opening angle θop is set to an opening angle between the tip 3and the tip 3 (that is, the slot opening angle).

Successively, an explanation will be given of torque generated by thebrushless DC motor of the embodiment in reference to a graph of FIG. 12.In the graph of FIG. 12, notation Tm designates the magnet torque, thenotation Tr designates the reluctance torque and notation Tt designatesa motor torque synthesized therewith, respectively. First, aninvestigation will be given of the magnetic torque Tm. According to thebrushless DC motor of the embodiment, the magnet torque Tm is generatedin a section substantially equal to the effective excitation openingangle θe. Because the effective magnetic pole opening angle θm and theeffective excitation opening angle θe are set to be substantially equalto each other. Next, an investigation will be given of the reluctancetorque Tr. The reluctance torque Tr constitutes a peak around a positionat which the effective magnetic pole opening angle θm of the rotor 4aligns with the effective excitation opening angle θe of the stator 1.That is, the reluctance torque Tr is provided with the peak at a phaseadvanced by 90° in electric angle and a phase lagged by 90° in electricangle relative to the magnetic torque Tm. The period is twice as much asthe period of the magnetic torque Tm.

Thereby, according to the brushless DC motor of the embodiment,reluctance torque Tr is strongly generated at a region at whichintensity of the magnetic torque Tm is reduced. Therefore, the motortorque Tt synthesized with the two torques, is substantially constantover a wide section as shown by the graph of FIG. 12. The graph of FIG.12 shows a quarter period (electric angle of 90°).

Further, the brushless DC motor of the embodiment is provided withthree-phase windings of U, V, and W as in FIG. 3, mentioned above.Therefore, when 120° electricity conduction is carried out, there are 6ways of electricity conduction patterns of U→V, U→W, V→W, V→U, W→U, andW→V. Therefore, there may be provided a section in which the motortorque Tt is substantially constant, per respective electricityconduction pattern, which is equal to or larger than 60°. As is apparentfrom the graph of FIG. 12, this is sufficiently satisfied. Therefore,the brushless DC motor of the embodiment can be driven with extremelysmall pulsation of the torque. By taking a consideration also to timingsof switching the electricity conduction patterns, the electricityconduction patterns may be switched at timings at which the torquevariation in switching is extremely small.

According to the above-described explanation, unexcited teeth in thestator 1 are made to be present discretely piece by piece. Further,therefore, the bridge opening angle θr of the rotor 4 is set inconformity with the opening angle of one piece of the tooth 2 (θr1 ofFIG. 2 or θr2 of FIG. 5). However, depending on ways of windings, it ispossible to constitute also a motor in which a plurality of continuousteeth 2 in the stator 1 simultaneously become unexcited tees. The bridgeopening angle θr of the rotor 4 in such a motor may be set as shown byFIG. 13 or FIG. 14. That is, the bridge opening angle θr is set to anopening angle for covering a total of a section in which unexcited teethare continuous. FIG. 13 shows an example of setting the bridge openingangle θr to the opening angle θr1 which does not include the tip 3 onthe both ends of the section. This corresponds to the example of FIG. 1and FIG. 2. Meanwhile, FIG. 14 shows an example of setting the bridgeopening angle θr to an opening angle θr2 including the tips 3 on bothends of the section. This corresponds to the example of FIG. 5.

The following is a general equation showing the bridge opening angle θrwhen a number of pieces of continuous unexcited teeth is not limited to1.(θtp×n)+θthNotation n is a number of the number of continuous unexcited teethsubtracted by 1 and is 0 or a natural number. Notation θtp in theequation designates the slot pitch angle of the stator 1 as mentioned inthe explanation of FIG. 2. Notation θth designates the tooth openingangle. An opening angle which does not include the tip 3 is used as thetooth opening angle θth in the case of the example of FIG. 13. Anopening angle including the tips 3 on the both sides is used as thetooth opening angle θth in the case of FIG. 14.

According to the explanation up to here, any of the permanent magnet 5is of a so-to-speak substantially circular arc type in which thepermanent magnet 5 is provided along the outer periphery of the rotor 4.However, the invention is applicable also to a constitution of otherthan the substantially circular arc type. FIG. 15 shows such an examplein which the invention is applied to a rotor 22 having a permanentmagnet 24 in a flat plate shape. According to the rotor 22, a magneticmember on an outer side of the permanent magnet 24 is more or lessthicker than those shown in FIG. 1 and the like. However, an effectsimilar to that in the case of the substantially circular arc type canbe achieved by slenderly forming a rib 26 from an end portion of thepermanent magnet 24 to a bridge 28 similar to the above-described.

As explained above in details, according to the brushless DC motor ofthe embodiment, the bridge opening angle θr of the rotor 4 is set inconformity with the opening angle of one piece or more of the teeth 2 inthe stator 1 (θr1 in FIG. 2 or FIG. 13, θr2 in FIG. 5 or FIG. 14).Therefore, a large portion of the magnetic flux generated by excitingthe stator coil (q axis in FIG. 8, contributing to reluctance torque)progresses to the inner side of the permanent magnet 5 by way of thebridge 8. Therefore, a magnet path thereof is directed from thepermanent magnet 5 to an outer side and is separate from a magnet pathof the magnetic flux interlinking with the stator coil (d axis in FIG.8, contributing to magnetic torque).

Therefore, the magnetic member of the rotor 4 is not magnetizedexcessively significantly by commonly providing the magnetic paths ofthe two magnetic fluxes. Therefore, the magnetic member of the rotor 4does not fall into the magnetic saturation. Therefore, the torque inproportion to power applied to the stator coil is provided and theenergy efficiency is excellent. Further, a waveform of the torque is awaveform which does not include almost any of harmonics components.Therefore, the properties of the motor are excellent and vibration ornoise produced by the harmonics can be reduced by that amount. Further,the cogging torque is easily reduced independently with inconsiderablymutual influence of the magnet torque and the reluctance torque andtherefore, a motor is easy to design. Specifically, the reduction of thecogging torque can be dealt with by pertinently setting the rib openingangle θd and the effective magnetic pole opening angle θm in the rotor4. Further, the magnetic flux density distribution at the gap betweenthe rotor 4 and the stator 1, is uniform in a range in correspondencewith the permanent magnet 5. Therefore, the adverse influence explainedby the bold line of the graph of FIG. 18 is eliminated.

Further, the brushless DC motor of the embodiment is further providedwith the rib 7 along the outer periphery of the rotor 4 between therespective permanent magnet 5 and the respective bridge 8. Further, therib 7 is made to be very slender. Therefore, the rib 7 is provided withhigh reluctance against the magnetic flux passing in the circumferentialdirection. Therefore, there is effectively restrained the leakagemagnetic flux (φr1, φs1 in FIG. 9, φr2, φs2 in FIG. 10) in the magneticflux of the permanent magnet 5 without interlinking with the stator coilvia the gap (φm1, φm2 in FIG. 9, φm3, φm4 in FIG. 10). Therefore, themagneto motive force of the permanent magnet 5 can effectively beutilized as the torque of the motor. Further, since the leakage magneticflux is small, the variation of the leakage magnetic flux at therotational position of the rotor 4 is also small. Thereby, the coggingtorque produced by the variation of the leakage magnetic flux can alsobe reduced. Particularly, when the permanent magnet 5 is of strong rareearth species, the cogging torque produced by the variation of theleakage magnetic flux is liable to increase and therefore, significanceof the effect is enormous.

Further, according to the brushless DC motor of the embodiment, theopening angle θd of the rib 7 is set to fall in the range specifiedbelow relative to the teeth interval opening angle θop of the stator 1.0.5×θop≦θd≦θopTherefore, the rib 7 is prevented from occupying an excessively largeportion of the outer periphery of the rotor 4 while ensuring an effectof restraining the leakage magnetic flux. Therefore, the permanentmagnet 5 or the bridge 8 is not improperly reduced and the function ofthe motor is not sacrificed.

Further, according to the brushless DC motor of the embodiment, themagnet torque and the reluctance torque are generated complimentarily(FIG. 12). Therefore, the variation of the synthesized torque can bereduced by a ratio of magnitudes of the two torques. Further, the rateper se of the reluctance torque occupied in the synthesized torque, cancomparatively be made large. Therefore, a rate of dependency on themagnet torque can be restrained by that amount. Thereby, the amount ofusing the permanent magnet is restrained. The significance isparticularly enormous when there is used a rare species magnet which isstrong but expensive. As described above, according to the embodiment,there is realized the brushless DC motor utilizing the reluctance torquein which by separating the magnetic paths by the magnetic flux of themagnetic torque and the magnetic flux of the reluctance torque, thedrawback by the mutual influence is excluded, the leakage of themagnetic flux of the permanent magnet is excluded as less as possibleand the magnet torque is made full use.

Further, the embodiment is merely an exemplification and does not limitthe invention at all. Therefore, the invention can naturally be improvedor modified variously within the range not deviated from a gist thereof.

For example, the number of the magnetic poles of the rotor and the shapeof the magnet, the number of teeth of the stator and the method ofwinding and the like are not limited to those exemplified above.Further, although according to the embodiment, there is shown the motorof the type in which the rotor is disposed at inside of the stator, theembodiment is applicable to a motor of a type in which a rotor isdisposed on an outer side of a stator. In that case, the magnetic flux(q axis in FIG. 8) carrying burden of the reluctance torque generated byexciting the stator coil, comes out to the outer side of the permanentmagnet by way of the bridge.

As is apparent from the above-described explanation, according to theinvention, there is provided the brushless DC motor utilizing thereluctance torque in which the magnetic paths are separated by themagnetic flux of the magnetic torque and the magnetic flux of thereluctance torque and the drawback produced by the mutual influence isexcluded. Further, there is provided the brushless DC motor utilizingthe reluctance torque in which leakage of the magnetic flux of thepermanent magnet is excluded as less as possible and the magnet torqueis made full use. Further, the brushless DC motor utilizing thereluctance torque according to the invention achieves a significantadvantage when used for a motor for driving an electric power steeringapparatus of a vehicle.

Second Embodiment

A detailed explanation will be given of embodiments embodying abrushless DC motor according to the invention in reference to theattached drawings as follows. According to the embodiment, the inventionis embodied as a brushless DC motor constituted by a stator of 12 slotsand a rotor of 4 poles.

A brushless DC motor according to the embodiment is constituted by astructure as shown by FIG. 16. A stator 52 of the brushless DC motorincludes 12 pieces of teeth 51 aligned at equal pitches in acircumferential direction. Meanwhile, a rotor 54 includes 4 pieces ofmagnets 53. The respective magnet 53 is formed by a shape of aso-to-speak substantially circular arc along an outer periphery of therotor 54. A respective magnet attaching hole 55 at the rotor 54 isformed to be longer than the magnet 53 in the circumferential direction.The respective magnet 53 is attached to the center of the respectivemagnet attaching hole 55 in the circumferential direction. Therefore,there are gaps at both ends of the respective magnet 53. The respectivemagnet attaching hole 55 is formed to be extremely proximate to theouter periphery of the rotor 54. Therefore, a magnetic member on anouter side of the respective magnet attaching hole 55 is extremelyslender. A portion of the magnetic member on the outer side of therespective magnet attaching holes 55 is referred to as a rib 56. Thereis present a bridge 57 for connecting a central portion of the rotor 54and the rib 56 between the magnet attaching hole 55 and the magnetattaching hole 55. Further, in FIG. 16, a coil of the stator 52 isomitted.

An explanation will be given of names of dimensions of respectiveportions in the rotor 54 of the brushless DC motor according to theembodiment in reference to FIG. 17. First, a half of a width in thecircumferential direction on an outer peripheral side of the magnet 53,is referred to as an effective magnetic pole width Wm. The effectivemagnetic pole width Wm is a distance of measuring from a center to anend in the circumferential direction on the outer peripheral side of themagnet 53 in a circular arc shape along the rib 56. Further, a length onan inner side of a portion of the rib 56 from one end of the magnet 53to an end of the magnet attaching hole 55, is referred to as a riblength Lr. Further, a width in the circumferential direction of thebridge 57 is referred to as a bridge width Wb. The bridge width Wb is ashortest linear distance between the contiguous magnet attaching holes55. Next, a length in a diameter direction of the bridge 57 is referredto as a bridge length Lb. The bridge length Lb is equal to a width inthe diameter direction of the magnet attaching hole 55. Further, a widthin the diameter direction of the rib 56 is referred to as a rib widthWr. When the width of the rib 56 is not constant, a width of a portionhaving a least width in a range on an outer side of the magnet 53, isdefined as a rib width Wr.

According too the brushless DC motor of the embodiment, the rib width Wris set to satisfy both of the following two equations. That is, the ribwidth Wr is set not to exceed a smaller value of a value given by theright hand side of Equation (1) and a value given by the right hand sideof Equation (2). $\begin{matrix}{{{Equation}\mspace{20mu} 1}\mspace{110mu}} & \; \\{{Wr} \leq \sqrt{\frac{R \times {Wm}}{{Bz}/{Bm}} \times {Lr}}} & (1) \\{{Wr} \leq {\frac{Q \times {Wb}}{{Bz}/{Bb}} \times \frac{( {{Lr} + {Wm}} )}{Lb}}} & (2)\end{matrix}$where,

-   R: a rate of a leakage magnetic flux at the rib portion to a    magnetic flux progressing from the magnet 53 to the stator 52-   Q: a rate of a leakage magnetic flux at the rib portion to a    magnetic flux passing from the stator tooth 51 to the bridge 57 of    the rotor 54-   Bz: a saturation magnetic flux density of the magnetic member of the    rotor 54-   Bm: a magnetic flux density of the rib 56 of the rotor 54 in the d    axis direction (radial direction of the rotor)-   Bb: a magnetic flux density of the bridge 57 of the rotor 54 in    driving the rotor

The reason of setting the rib width Wr in such a way, resides in thefollowing point. That is, the rib width Wr significantly influences onthe torque generated by the brushless DC motor. Because although themagnetic flux of the magnet 53 induces the magnet torque by interlinkingwith the stator 52, a portion of the magnetic flux unavoidably leaks atthe rib 56. Therefore, the magnitude of the magnetic torque iscontrolled by large or small of the leakage magnetic flux at the rib 56.Further, large or small of the leakage magnetic flux is significantlycontrolled by the rib width Wr. The same goes with the reluctancetorque. That is, although the excitation magnetic flux of the stator 52induces the reluctance torque by passing the bridge 57 and interlinkingwith the axis core portion, a portion of the magnetic flux unavoidablyleaks at the rib 56. Therefore, the magnitude of the reluctance torqueis controlled by large or small of the leakage magnetic flux at the rib56. Further, large or small of the leakage magnetic flux issignificantly controlled by the rib width Wr.

A further explanation will be given of the magnetic flux from the magnet53 in the above-described magnetic fluxes in reference to FIG. 18 andFIG. 19. As shown in FIG. 18 by subjecting a vicinity of the outerperiphery of the rotor 54 to linear development, a large portion of themagnetic flux of the magnet 53 is interlinked with the stator 52 via theair gap. The magnetic flux φm relates to the magnet torque. A magneticflux density in the diameter direction of the rib 56 by the magneticflux φm is designated by notation Bm. Here, a portion of the magneticflux of the magnet 53 passes the rib 56 and flows to the contiguousmagnet 53 without interlinking with the stator 52. This does not relateto the magnetic torque and therefore is a leakage magnetic flux φr1. Aremainder produced by subtracting the leakage magnetic flux φr1 from thetotal magnetic flux of the magnet 53 is the magnetic flux φm. A magneticflux density in the circumferential direction of the rib 56 by theleakage magnetic flux φr1, is designated by notation Br1. Further, inFIG. 18 (also similar to FIG. 20 mentioned below), the rib width Wr isdrawn to be bolder than actual.

The magnetic flux density Bm is controlled by the rib width Wr as shownby a graph of FIG. 19. Because the leakage magnetic flux φr1 iscontrolled by the rib width Wr. That is, as shown by a curve of a brokenline, when the rib width Wr is large, the magnetic flux density Bm issmall. Therefore, the magnet torque is not increased. Because when therib width Wr is large, reluctance or the rib 56 in the circumferentialdirection is small and the leakage magnetic flux φr1 is increased bythat amount. In contrast thereto, as shown by a curve of a bold line,when the rib width Wr is small, the magnetic flux density Bm is large.Therefore, large magnet torque is achieved. Because when the rib widthWr is small, the reluctance in the circumferential direction of the rib56 is large and the leakage magnetic flux φr1 is reduced by that amount.Further, a similar effect is achieved when the rib length Lr is large,similar to that when the rib width Wr is small. Further, a similareffect is achieved when the rib length Lr is small similar to that whenthe rib width Wr is large. Further, the abscissa x in FIG. 19 designatesa phase angle in the rotor 54.

Next, a further explanation will be given of the magnetic fluxinterlinking with the rotor 54 from the stator 52 in reference to FIG.20. As shown in FIG. 20 by subjecting the vicinity of the outerperiphery of the rotor 54 to the linear development, a large portion ofthe magnetic flux interlinking with the rotor 54 from the stator 52 viathe air gap, flows to the axis core portion by passing the bridge 57.The magnetic flux φb relates to the reluctance torque. A magnetic fluxdensity in the diameter direction of the bridge 57 by the magnetic fluxφb is designated by notation Bb. Here, a portion of the magnetic fluxprogressing from the stator 52 to the rotor 54, passes the rib 56 andreturns to the stator 52 without interlinking with the bridge 57. Thisdoes not relate to the reluctance torque and therefore is a leakagemagnetic flux φr2. A remainder produced by subtracting the leakagemagnetic flux φr2 from the total magnetic flux progressing from thestator 52 to the rotor 54, is designated by a magnetic flux φb. Amagnetic flux density in the circumferential direction of the rib 56 bythe leakage magnetic flux φr2 is designated by notation Br2.

Also the magnetic flux density Bb is controlled by the rib width Wr andthe rib length Lr similar to the above-described magnetic flux densityBm. Because the leakage magnetic flux φr2 is controlled by the rib widthWr and the rib length Lr. That is, the magnetic flux density Bb is smallwhen the rib width Wr is large (the rib length Lr is small). Therefore,the reluctance torque is not increased. In contrast thereto, themagnetic flux density Bb is large when the rib width Wr is small (therive length Lr is large). Therefore, the large reluctance torque isachieved.

Next, an investigation will be given of the motor torque constituting atotal of the magnetic torque and the reluctance torque. Consider here anequivalent two-phase machine produced by converting inductance ofthree-phase windings provided to the stator from fixed coordinates torotation coordinates. Then, the motor torque Tt is generally representedby the following equation. $\begin{matrix}{{Tt} = {{P \times \sqrt{\frac{3}{2}} \times \Phi\; m_{MAX} \times {Iq}} + {P \times ( {{Ld} - {Lq}} ) \times {Id} \times {Iq}}}} & {{Equation}\mspace{14mu} 2}\end{matrix}$

-   P: pole pair number    φm_(MAX): a maximum value of φm-   Id (d axis current): excitation current of a coil of the tooth 51    opposed to a center of the magnetic pole (center in the    circumferential direction of the magnet 53) of the rotor 54-   Iq (q axis current): excitation current of a coil of the tooth 51    opposed to between the magnetic poles (that is, the bridge 57) of    the rotor 54-   Ld: inductance of the coil of the tooth 51 opposed to the center of    the magnetic pole of the rotor 54-   Lq: inductance of the coil of the tooth 51 opposed to between the    magnetic poles of the rotor 54

In Equation 2, the first term corresponds to the magnet torque and thesecond term corresponds to the reluctance torque. It is known therebythat the reluctance torque is proportional to a magnitude of adifference between Ld and Lq. Further, in Equation 2, even when (Ld−Lq)is negative, in the case in which Id is negative and Iq is positive,signs of the first term and the second term coincide with each other.Therefore, the two torques are increased together. Here, inductance ofthe coil of the stator is proportional to a change over time of anamount of the magnetic flux interlinking with the coil. Therefore, whenthe leakage magnetic flux is reduced, the amount of the magnetic fluxinterlinking with the coil is relatively increased and reluctance torqueincreased.

The magnitude of the difference between Ld and Lq is shown by a graph ofFIG. 21 by the rib width Wr (or the rib length Lr) and a rotationalangle φx of the rotor 54. FIG. 21 shows the ordinate by an absolutevalue as a diagram representing the magnitude of the inductance. It isknown from the graph that |Ld−Lq| is controlled by the rib width Wr.That is, as shown by a curve of a broken line, when the rib width Wr islarge, |Ld−Lq| is small. Therefore, the reluctance torque is notincreased. In contrast thereto, as shown by a curve of a bold line, whenthe rib width Wr is small, |Ld−Lq| is large. Therefore, the largereluctance torque is achieved. Further, an effect is achieved when therib length Lr is large similar to that when the rib width Wr is small.Further, an effect is achieved when the rib length Lr is small similarto that when the rib with Wr is large. Further, notation H1 in the graphof FIG. 21 designates an average value of |Ld−Lq|when the rib width Wris small. Notation H2 designates an average value of |Ld−Lq| when therib width Wr is large.

The above-described is synthesized as follows. That is, in a state inwhich the reluctance of the rotor 54 is low in view from the arbitrarytooth 51 of the stator 52, the interlinking magnetic flux from the tooth51 of the rotor 54 is naturally increased. However, when the leakagemagnetic flux φr2 is large, regardless of the rotational angle of therotor 54, the interlinking magnetic flux from the tooth 51 to the rotor54 is not so much changed. This signifies that the torque of the rotor54 which is going to move to a position at which the interlinkingmagnetic flux from the tooth 51 to the rotor 54 is the largest, that is,the reluctance torque is small. Therefore, large or small of the leakagemagnetic flux φr2 influences on the magnitude of the reluctance torque.

An explanation will successively be given of a condition to be satisfiedby the rib width Wr. The rib width Wr may be small to a degree by whichthe rib 56 reaches or exceeds the saturation magnetic flux density bythe leakage magnetic fluxes φfr1 and φr2. Because when the rib width Wris small as described above, the reluctance in the circumferentialdirection of the rib 56 is very large and the leakage magnetic fluxesφr1 and φr2 are restrained. Further, because the magnitudes of theleakage magnetic fluxes φr1 and φr2 are not so much changed under anysituation.

First, an investigation will be given of a condition based on themagnetic flux of the magnet 53. The magnetic flux density Bm in theradial direction (d axis direction) of the rib 56 is represented by thefollowing equation by using the magnetic flux φm interlinking with thestator 52 from the magnet 53 via the air gap and related to the magnettorque, the effective magnetic pole width Wm and a thickness (laminatedthickness) Lh of the rotor 54. $\begin{matrix}{{Bm} = \frac{\phi\mspace{11mu} m}{{Wm} \times {Lh}}} & {{Equation}\mspace{14mu} 3}\end{matrix}$

Further, the magnetic flux density Br1 in the circumferential directionof the rib 56 is represented by the following equation by using theleakage magnetic flux φr1 by the rib 56 in the magnetic flux of themagnet 53, the rib width Wr and the thickness (laminated thickness) Lh.$\begin{matrix}{{Br1} = \frac{\phi\mspace{11mu}{rr1}}{{Wr} \times {Lh}}} & {{Equation}\mspace{14mu} 4}\end{matrix}$

Here, a rate (φr1/φm) of the leakage magnetic flux φr1 to the magneticflux φm related to the magnet torque is represented by notation R. Whenthe above-specified R is used Equation 4 is represented as follows.$\begin{matrix}{{Br1} = \frac{R \times \phi\mspace{11mu} m}{{Wr} \times {Lh}}} & {{Equation}\mspace{14mu} 5}\end{matrix}$

Meanwhile, a condition by which the rib 56 reaches to be equal to orlarger than the saturation magnetic flux density Bz by the leakagemagnetic flux φr1, is represented by the following equation by using aratio Bz/Bm of the magnetic flux density Bm in the d axis direction tothe saturation magnetic flux density Bz. $\begin{matrix}{{Br1} \geq {\frac{Bz}{Bm} \times {Bm}}} & {{Equation}\mspace{14mu} 6}\end{matrix}$

The following equation is provided by substituting Equation 3 andEquation 5 therefor. $\begin{matrix}{\frac{R \times \phi\; m}{{Wr} \times {Lh}} \geq {\frac{Bz}{Bm} \times \frac{\phi\; m}{{Wm} \times {Lh}}}} & {{Equation}\mspace{14mu} 7}\end{matrix}$

The following equation is provided by solving the above-describedinequality with regard to the rib width Wr. $\begin{matrix}{{Wr} \leq \frac{R \times {Wm}}{{Bz}/{Bm}}} & {{Equation}\mspace{11mu} 8}\end{matrix}$

Consider here of the reluctance of the rib 56. The reluctance of the rib56 to the leakage magnetic flux φr1 is proportional to the rib length Lrand inversely proportional to the rib width Wr. By taking the fact intoconsideration, Equation 8 finally becomes the following equation.$\begin{matrix}{{Wr} \leq {\frac{R \times {Wm}}{{Bz}/{Bm}} \times \frac{Lr}{Wr}}} & {{Equation}\mspace{14mu} 9}\end{matrix}$

Therefore, finally, by multiplying both sides of Equation 9 by Wr andtaking a root, Equation (1) of Equation 1, mentioned above, is provided.Therefore, the rib width Wr must be equal to or lower than a value givenby the right hand side of Equation (1) of Equation 1.

Next, an investigation will be given of a condition based on themagnetic flux interlinking with the rotor 54 from the stator 52. Themagnetic flux density Bb in the diameter direction (q axis direction) ofthe bridge 57 is represented by the following equation by using themagnetic flux φb interlinking with the axis core portion of the rotor 54from the stator 52, the bridge width Wb and the laminated thickness Lhof the rotor 54. $\begin{matrix}{{Bb} = \frac{\phi\; b}{\;{{Wb} \times {Lh}}}} & {{Equation}\mspace{14mu} 10}\end{matrix}$

Further, the magnetic flux density Br2 in the circumferential directionof the rib 56 is represented by the following equation by using theleakage magnetic flux φr2 by the rib 56 in the magnetic flux of thestator 52, the rib width Wr and the laminated thickness Lh.$\begin{matrix}{{Br2} = \frac{\phi\;{r2}}{{Wr} \times {Lh}}} & {{Equation}\mspace{14mu} 11}\end{matrix}$

Here, a rate (φr2/φb) of the leakage magnetic flux φr2 to the magneticflux φb related to the reluctance torque, is represented by notation Q.When the above-specified Q is used, Equation 11 is represented asfollows. $\begin{matrix}{{Br2} = \frac{Q \times \phi\; b}{{Wr} \times {Lh}}} & {{Equation}\mspace{14mu} 12}\end{matrix}$

Meanwhile, a condition by which the rib 56 reaches to be equal to orlarger than the saturation magnetic flux density Bz by the leakagemagnetic flux φr2, is represented by the following equation by using themagnetic flux density Bb in the q axis direction and a ratio Bz/Bb ofthe magnetic flux density Bb in the q axis direction to the saturationmagnetic flux density Bz. $\begin{matrix}{{Br2} \geq {\frac{Bz}{Bb} \times {Bb}}} & {{Equation}\mspace{14mu} 13}\end{matrix}$

The following equation is provided by substituting Equation 10 andEquation 12 therefor. $\begin{matrix}{\frac{Q \times \phi\; b}{{Wr} \times {Lh}} \geq {\frac{Bz}{Bb} \times \frac{\phi\; b}{\;{{Wb} \times {Lh}}}}} & {{Equation}\mspace{14mu} 114}\end{matrix}$

The following equation is provided by solving the above-describedinequality with regard to the rib width Wr. $\begin{matrix}{{Wr} \leq \frac{Q \times W\; b}{{Bz} \times {Bb}}} & {{Equation}\mspace{14mu} 15}\end{matrix}$

Consider here of the reluctance of the rib 56. The leakage magnetic fluxφr2 passes not only a portion of the rib 56 between the magnet 53 andthe bridge 57 (length Lr) but also a portion thereof in contact with themagnet 53 (length Wm). Therefore, the magnetic reluctance of the rib 56to the leakage magnetic flux φr2 is proportional to a sum of the riblength and effective magnetic pole width (Lr+Wm) and inverselyproportional to the rib width (Wr). By taking the fact intoconsideration, finally, Equation (2) of Equation 1, mentioned above, isprovided. Therefore, the rib width Wr must be equal to or smaller thanthe value given by the right hand side of Equation (2) of Equation 1,mentioned above.

From the above-described, when a consideration is given to both of themagnetic flux of the magnetic torque and the magnetic flux of thereluctance torque, the rib width Wr must be equal to or smaller than asmaller value of the value given by the right hand side of Equation (1)of Equation 1 and the value given by the right hand side of Equation (2)of Equation 1. Therefore, according to the brushless DC motor of theembodiment, the rib width Wr is set as described above. Therefore,according to the brushless DC motor of the embodiment, the leakagemagnetic fluxes φr1 and φr2 per se are very small and there is almost novariation thereof. Further, notations “R” and “Q” used in the Equationsare parameters which can be set in designing the motor.

An explanation will be given here of Bz/Bm and Bz/Bb in the respectiveequations of Equation 1. For that purpose, an explanation will firstlygiven of a magnetizing property of a silicon steel plate constituting arepresentative magnetic member used in an iron core of a motor of thiskind. An explanation will be given here of four kinds of samples ofsample E: 50A10000 (JIS), sample F: 50A400 (JIS), sample G: 35A230 (JIS)and sample H: 6.5% Si silicon steel plate. As shown by a graph of amagnetization curve of FIG. 22, a saturation magnetic flux density Bz ina general region of using the silicon steel plates, falls in a range of1.8 through 2.2 tesla.

Further, when the magnetic flux density Bm in the d axis direction andthe magnetic flux density Bb in the q axis direction, mentioned above,are excessively proximate to the saturation magnetic flux density Bz, itsignifies that the energy loss is large. Because the magnetic fluxdensities Bm and Bb are not so much increased with regard to themagnetizing force. Therefore, the magnetic flux densities Bm and Bb areto be set not to be proximate to the saturation magnetic flux density Bzregardless of a situation of rotating the brushless DC motor. For thatpurpose, set values of the magnetic flux densities Bm and Bb are to beset to be equal to or smaller than 1 tesla. Meanwhile, when the setvalues of the magnetic flux densities Bm and Bb are excessively small,the function of the motor is not achieved sufficiently. Therefore, theset values of the magnetic flux densities Bm and Bb are made to fall ina range of 0.5 through 1.0 tesla. Thereby, ranges to be taken by Bz/Bmand Bz/Bb become 1.8 through 4.4.

According to the brushless DC motor of the embodiment, the waveform ofthe torque is as shown by FIG. 23. The graph is for a case in which theeffective excitation pole opening angle is set to be substantially equalto the excitation magnetic pole pitch, showing a quarter period of theelectric angle. The magnet torque Tm is generated substantially in asection equal to the effective excitation magnetic pole opening angle.The reluctance torque Tr is generated around a position at which themagnet 53 of the rotor 54 is aligned to the effective excitation tooth51 of the stator 52. Therefore, the reluctance torque Tr is providedwith a period twice as much as that of the magnet torque Tm in a stateof advancing the phase by 90° in the electric angle. Therefore, themagnet torque Tm and the reluctance torque Tr compensate for each other.

Further, since the rib width Wr of the rotor 54 is set as describedabove, both of the magnet torque Tm and the reluctance torque Tr arehardly varied by influence of the leakage magnetic fluxes φr1 and φr2.Therefore, when peak values of the two torques are the same, thesynthesized motor torque Tt is substantially constant. Further, when athree-phase motor of 120° electricity conduction is considered, themotor torque Tt may be provided with an effective section of 60° withregard to 6 of the electricity conduction patterns. Therefore, whenelectricity conduction is switched at a timing at which the motor torqueTt is constant, the motor torque of the three-phase motor becomeextremely smooth having almost no pulsation.

Further, the magnet torque Tm is dominant with regard to the motortorque Tt depending on the brushless DC motor (refer to FIG. 24). In thecase of such a brushless DC motor, only Equation (1) of Equation 1 maybe considered. The rib width Wr in that case, may be equal to or smallerthan the value given by the right hand side of Equation (1) ofEquation 1. Or, the reluctance torque Tr may be dominant with regard tothe motor torque Tt depending on the brushless DC motor (refer to FIG.25). In the case of such a brushless DC motor, only Equation (2) ofEquation 1 may be considered. That is, the rib width Wr in that case maybe equal to or smaller than the value given by the right hand side ofEquation (2) of Equation 1. Here, the magnet torque Tm or the reluctancetorque Tr is dominant as specified below. That is, in graphs of FIG. 23through FIG. 25, when an integrated intensity of the magnet torque Tm islarger than an integrated intensity of the reluctance torque Tr, themagnet torque Tm is dominant. In the inverse case, the reluctant torqueTr is dominant.

Further, depending on the brushless DC motor, there is a case in whichthe magnet 53 of the rotor 54 is attached not to the center in thecircumferential direction of the magnet attaching hole 55 but attachedto be deviated therefrom. The effective magnetic pole width Wm withregard to such a magnetic pole may be defined as follows. Strictlythinking, the definition depends on with which of two of contiguousmagnets d axis the magnetic flux from the magnet 53 is interlinked. Thatis, the effective magnetic pole width Wm is to be defined from aboundary of a magnetic flux interlinking with the right contiguousmagnet and magnetic flux interlinking with the left contiguous magnet toan end portion thereof. However, as shown by FIG. 26, in the case of themagnet 53 deviated to the left side in the drawing, much of theinterlinking magnetic flux is going to flow to the left contiguous oneconstituting low reluctance in view of a magnetic path. However, magnetsof contiguous magnetic poles are arranged to be opposed to each otherrelatively and therefore, when a pair of the magnetic poles areconstituted, a magnetic flux amount remains almost unchanged. Therefore,the boundary of the effective magnetic pole width Wm of the magneticpole may be determined by the center in the circumferential direction ofthe magnet attaching hole 55.

Next, an explanation will be given of a case of a brushless DC motorhaving the magnet 63 in a linear shape as shown by FIG. 27. Also in thecase of the rotor 64 in such a shape, the bridge width Wb and the bridgelength Lb may be considered similar to the above-described. With regardto the rib length Lr and the rib width Wr, a rib 66 is defined by aportion of a magnetic member of a magnet attaching hole 65 having aleast width. It is necessary to replace the effective magnetic polewidth Wm not by a value from a center to an end of the magnet 63 per sebut a value in consideration of reluctance. Specifically, Wm in Equation(1) of Equation 1, is defined as a length from the center of the magnet63 to a boundary thereof with the rib 66. Because the magnetic flux (daxis) of the magnet 63 is widened in the circumferential direction at amagnetic member region 68 on an outer side of the magnet 63 andprogresses to the stator. Wm in Equation (2) of Equation 1 is defined asa length realizing reluctance the same as reluctance in thecircumferential direction of the magnetic member region 68 by a widththe same as the rib width Wr. This is considerably short and when awidth in a diameter direction of the magnetic member region 68 isconsiderably wider than the rib width Wr, the length may be disregardedand the equation may be considered to have only the rib length Lr.

As explained above in details, according to the brushless DC motor ofthe embodiment, the width Wr of the rib 56 on an outer peripheral sideof the magnet 53 is defined to be equal to or smaller than the valuegiven by the right hand side of Equation (1) of Equation 1. Further, thewidth Wr is defined to be equal to or smaller than the value given bythe right hand side of Equation (2) of Equation 1. Therefore, the rib 56reaches the saturation magnetic flux density Bz easily by the leakagecomponent φr1 in the magnetic flux of the magnet 53 or also by theleakage component φr2 in the magnetic flux interlinking with the rotor54 from the stator 52. Therefore, the leakage magnetic flux is hardlyvaried under any rotational situation. Therefore, the magnet torque andthe reluctance torque are not influenced by the variation of the leakagemagnetic flux. In this way, there is realized the brushless DC motorwhich hardly brings about pulsation of a torque produced by thevariation of the leakage magnetic flux in the synthesized motor torque.Therefore, the two torques can be utilized with excellent balance.

The fact is significant in the case of the brushless DC motor using astrong magnet of rare earth species or the like. In such a motor, awidth of a variation in the leakage magnetic flux φr1 is liable toincrease by an amount of the large magneto motive force of the magnet.By constituting the motor as in the embodiment, even in the case ofusing such a magnet, influence by the variation in the leakage magneticflux φr1 can be minimized.

According to the brushless DC motor of the embodiment, Bz/Bm and Bz/Bbare set in a range of 1.8 through 4.4. Therefore, the magnetic fluxdensity Bm in the d axis direction and the magnetic flux density Bb inthe q axis direction do not approach considerably to the saturationmagnetic flux density Bz. Therefore, there is realized a structure ofthe brushless DC motor having a small amount of the energy loss producedby the magnetic saturation of the magnetic member of the rotor 54.

Further, according to the brushless DC motor of the embodiment, themagnetic path (d axis) of the magnet torque and the magnetic path (qaxis) of the reluctance torque are separated from each other at thevicinity of the air gap. Because of the fact and also owing to the smallamount of the leakage magnetic flux, mentioned above, the two torquesare less reduced. Further, separation of the paths of the two magneticfluxes, also restrains harmonics of the magnet torque. Becausedeflection of the magnetic flux of the magnet torque caused by themagnetic flux of the reluctance torque is inconsiderable. Thereby,generation of sound and vibration is also prevented.

Further, the embodiment is only a simple exemplification and does notlimit the invention at all. Therefore, the invention can naturally beimproved or modified variously within the range not deviated from gistthereof. For example, the number of the magnet poles of the rotor, theshape of the magnet, the number of the teeth of the stator and the likeare not limited to those exemplified. Further, although according to theembodiment, there is shown the motor of the type in which the rotor isdisposed at inside of the stator, the embodiment is applicable to amotor of a style in which a rotor is disposed on an outer side of astator. In that case, a magnetic flux generated by exciting a statorcoil and carrying burden of a reluctance torque, come out to an outerside of a magnet via a bridge.

As is apparent from the above-described explanation, according to theinvention, there is provided the brushless DC motor having the structurein which in the brushless DC motor utilizing both of the magnetic torqueand the reluctance torque, adverse influence by the leakage magneticflux is made as small as possible and the two torques are effectivelyutilized with excellent balance. Further, the energy caused by themagnetic saturation is also reduced. Further, the brushless DC motorutilizing the reluctance torque according to the invention, achieves asignificant advantage when used in a motor for driving an electric powersteering apparatus of a vehicle.

Third Embodiment

A detailed explanation will be given of embodiments embodying theinvention in reference to the attached drawings as follows.

A brushless DC motor according to the embodiment is constituted as shownby FIG. 28. FIG. 28 is shown by omitting a lower half of the motor. Arotor 80 of FIG. 28 is provided with 4 pieces of magnets 81 and a polepair number is 2. Therefore, an electric angle with regard to the rotor80 is twice as much as a geometrical angle. The rotor 80 is formed with4 of magnet attaching holes 82. The respective is attached with a singleone of the magnet 81. There is present a magnetic member region 83 alsoon an outer side of the respective magnet 81 in the rotor 80. Further,there is present a bridge 84 connecting an outer side and an inner sideof the magnet 81 by a magnetic member between the contiguous magnets 81.A stator 90 of FIG. 28 includes 12 pieces of teeth 91. Although windingsare provided actually to the respective teeth 91, the windings areomitted in FIG. 28.

A further explanation will be given of the rotor 80 in FIG. 28 inreference to FIG. 29. FIG. 29 is shown by taking out the rotor 80 inFIG. 28. According to the rotor 80, an angle from a middle to acontiguous middle of the magnets 81, is 180° in electric angle. Further,an angle of a portion thereof occupied by the magnet 81, is referred toas effective magnetic pole opening angle θm. Both ends of the effectivemagnetic pole opening angle θm are intersections with radii passing bothends of the magnet 81 on an outer peripheral side thereof. Further, anangle from an end of the magnet attaching hole 82 to a middle of themagnet 81, corresponds to a half of a bridge opening angle θr. It isapparent that a sum of the angles on both sides is equal to the openingangle of the bridge 84. A gap between the effective magnetic poleopening angle θm and each of the portions of (½) θr on the both sides,corresponds to a gap at a vicinity of the end portion of the magnetattaching hole 82. Although the gap is drawn exaggeratingly in FIG. 29,the gap is actually smaller from reason, mentioned later. That is, alarge portion (equal to or larger than 83.3%, more preferably, equal toor larger than 90%) of a supplementary angle of the effective magneticpole opening angle θm is occupied by a bridge opening angle θr.

An explanation will be given of a situation of interlinking magneticfluxes in the rotor 80 in reference to FIG. 30. First, an explanationwill be given of the magnetic flux related to the magnet torque. Themagnetic flux related to the magnet torque is interlinked as shown by anarrow mark of d axis in FIG. 30. That is, the magnetic flux passes 2 ofthe magnets 81 and the magnetic member regions 83 on outer sides thereofand does not pass the bridge 84. Meanwhile, the magnetic flux related tothe reluctance torque is interlinked as shown by an arrow mark of q axisin FIG. 30. That is, the magnetic flux passes the bridges 84 at 2locations and does not pass the magnet 81 and the magnetic member region83 on the outer side. Thereby, the magnetic member region 83 on theouter side is a path of the magnetic flux mainly related to the magnettorque. Meanwhile, the bridge 84 is a path of the magnetic flux mainlyrelated to the reluctance torque. Therefore, in order to utilize thereluctance torque as effectively as possible, it is necessary thatreluctance in a radius direction of the bridge 84 is as small aspossible. A large portion of the supplementary angle of the effectivemagnetic pole opening angle θm is occupied by the bridge opening angleθr for such a reason.

A synthesized torque Tt of this kind of the motor is generallyrepresented by the following equation. $\begin{matrix}\begin{matrix}{{Tt} = {{P \times \sqrt{\frac{3}{2}} \times \Phi\; m_{MAX} \times {Iq}} +}} \\{P \times ( {{Ld} - {Lq}} ) \times {Id} \times {Iq}}\end{matrix} & {{Equation}\mspace{14mu} 16}\end{matrix}$

-   P: a pole pair number-   φm_(MAX): a maximum value of the magnetic flux related to the magnet    torque-   Iq: current exciting the q axis direction of the rotor 80-   Id: current exciting the d axis direction of the rotor 80-   Lq: inductance of windings of the tooth 91 opposed to the q axis    direction of the rotor 80-   Ld: inductance of windings of the tooth 91 opposed to the d axis    direction of the rotor 80

The first term of the right hand side of the equation corresponds to themagnet torque in proportion to a magnetic flux amount of the magnet 81.The second term corresponds to the reluctance torque in proportion to adifference of inductances between the d axis and the q axis. A sum ofthe magnet torque and the reluctance torque is the synthesized torqueTt.

Consider here a situation of the torque when the effective magnetic poleopening angle θm of the magnet 81 is changed and the bridge openingangle θr is also changed in accordance therewith. When the inventorscarry out a simulation, a result shown in a graph of FIG. 31 is providedwith regard to the inductances Lq and Ld. According to the graph, theabscissa designates the effective magnetic pole opening angle θm and theordinate designates inductance. Further, three ways of curves of Lq, Ld,and Lq−Ld are drawn in the graph.

In taking a look at a case in which the effective magnetic pole openingangle θm is 180° (electric angle) in the graph, there is not adifference between Lq and Ld and therefore, Lq−Ld becomes null.Therefore, the reluctance torque is not generated. There is not adifferentiation between the d axis and q axis in a magnetic flux path inthis case and all of the magnetic fluxes detour the magnet 11. BecauseLq and Ld coincide with each other at a low value thereby. Further, thatthe effective magnetic pole opening angle θm is 180° in electric angle,is that there is not present the bridge 84 and there is not present amagnetic flux path for the reluctance torque.

Conversely, in taking a look at a case in which the effective magneticpole opening angle θm is 0°, there is not still a difference between theLq and Ld and therefore, Lq−Ld becomes null. Therefore, the reluctancetorque is not generated. In this case, there is not the magnet 81, allof the magnetic fluxes pass the magnetic member and therefore, there isnot still a differentiation between the d axis and the q axis.Therefore, Lq and Ld coincide with each other at a high value.

When the behavior is analyzed with respect to a magnetic field and amagnetic flux distribution in the air gap is calculated, there is knowna situation of a case in which the effective magnetic pole angle θmfalls in a range of 0° through 180° in electric angle. When theinductances Lq and Ld are calculated in this way, it is known that Lq−Ldbecomes a maximum when the effective magnetic pole opening angle θm is90° (electric angle). The curve of Lq−Ld in the graph of FIG. 31 showsthe fact.

When the torque is calculated by applying the result to Equation 16,mentioned above, a graph as shown by FIG. 32 is provided. The reluctancetorque Tr in the graph is provided with a shape the same as that of thecurve of Lq−Ld in FIG. 31. Naturally, the larger the number of themagnet 81, the stronger the magnet torque Tm and therefore, there isconstituted a curve rising to the right in the graph. The synthesizedtorque Tt is the total of the reluctance torque Tr and the magnet torqueTm.

In taking a look at a location at which the effective magnetic poleopening angle θm is 180° (electric angle) in the graph, all of thesynthesized torque Tt depends on the magnetic torque Tm and there is notthe reluctance torque Tr. Conversely in taking a look at a location atwhich the effective magnetic pole opening angle θm is 0°, the magnetictorque Tm is null. Because the magnet 81 is not present. Further, thereluctance torque Tr is also null from the above-described reason.Therefore, the synthesized torque Tt is null.

Hence, consider that the effective magnetic pole opening angle θm isreduced from 180° (electric angle) little by little. In this case, themagnetic torque Tm is going to be reduced with a reduction in theeffective magnetic pole opening angle θm. Because the magnetic fluxamount of the magnet 81 is going to be reduced. However, the reluctancetorque Tr is conversely increasing. Further, an increase in thereluctance torque Tr is more than a reduction in the magnet torque Tm.Therefore, the synthesized torque Tt is increasing by the reduction inthe effective magnetic pole opening angle θm. Such a situation iscontinued until the effective magnetic pole opening angle θm reaches150° (electric angle). When the effective magnetic pole opening angle θmbecomes smaller than 150° (electric angle), the reduction in the magnettorque Tm becomes conversely more than the increase in the reluctancetorque Tr. Therefore, the synthesized torque Tt constitutes a maximumvalue at a location at which the effective magnetic pole opening angleθm is 150° (electric angle) and tends to reduce thereafter. Further, ata location at which the effective magnetic pole opening angle θm is 120°(electric angle), there is constituted the synthesized torque Tt thesame as that when the effective magnetic pole opening angle θm is 180°(electric angle). The synthesized torque Tt thereafter becomes a valuelower than that when the effective magnetic pole opening angle θm is180° (electric angle).

As described above, there is present a region for providing thesynthesized torque Tt stronger than that when the effective magneticpole opening angle θm is 180° (electric angle) in a range in which theeffective magnetic pole opening angle θm is smaller than 180° (electricangle) and larger than 120° (electric angle). The nearer the effectivemagnetic pole opening angle θm to 150° (electric angle), the moresignificant is the tendency of increasing the torque. A significantdifference in comparison with the conventional motor actually, falls ina range of the effective magnetic pole opening angle θm from 127°(electric angle) to 173° (electric angle) Naturally, the narrower thanrange, the more advantageous. By setting the effective magnetic poleopening angle θm in such a range, in comparison with the brushless DCmotor having the effective magnetic pole opening angle θm of 180°(electric angle), there is provided the synthesized torque Tt which israther strong by a less amount of using the magnet 81.

Hence, in order to actually generate the above-described synthesizedtorque in the brushless DC motor of the embodiment in which theeffective magnetic pole opening angle θm is made to be smaller than 180°(electric angle), the motor must be driven to generate the reluctancetorque. For such a purpose, a phase of excitation current applied to thewindings of the stator 90 must be a phase more advanced than a phase ofso-to-speak induced voltage of the motor as shown by FIG. 33. This isapparent because the d axis current Id is put to the second term of theright hand side of Equation 16, mentioned above.

Hence, an explanation will be given of an advancing phase of theexcitation current. With regard to excitation from the stator 90, themagnet flux is easy to pass in the q axis direction of the rotor 80(refer to FIG. 30) and the inductance Lq is large. Because the magneticmember is present continuously in the radius direction. In contrastthereto, the magnetic flux is difficult to pass in the d axis directionof the rotor 80 and the inductance Ld is small. Therefore, (Ld−Lq) ofthe second term of the right hand side of Equation 16 is negative. Inorder to achieve the strong synthesized torque Tt, the second term(reluctance torque) needs to be positive. For that purpose, when the qaxis current Iq is positive, the d axis current Id must be negative andconversely, when the q axis current Iq is negative, the d axis currentId must be positive.

FIG. 34 and FIG. 35 represent the fact as vector diagrams with the daxis as a reference. FIG. 34 shows a case in which the d axis current Idis negative. FIG. 35 shows a case in which the d axis current Id ispositive. It is known from the vector diagrams that there is neededcurrent having a phase angle of θ1 (FIG. 34) or θ2 (FIG. 35) relative tothe q axis current Iq. This is the advancing phase of the excitationcurrent. That is, as an advancing phase angle θf in the waveform diagramof FIG. 33, mentioned above, θ1 of FIG. 34 or θ2 of FIG. 35 may be used.

A further explanation will be given of the advancing phase angle incomparison with the structure of the brushless DC motor. As shown byFIG. 36, application of the excitation current having the advancingphase angle signifies that excitation of the tooth 91 is started earlierthan when the bridge 84 of the rotor 80 is opposed to a front face ofthe tooth 91 of the stator 90 (advancing angle θf) as shown by FIG. 36.At this occasion, the tooth 91 and the bridge 84 are angularlyoverlapped (angle θw) or extremely proximate to each other andtherefore, the excitation magnetic flux Φ of the tooth 91 is interlinkedeasily with the bridge 84. Because the bridge 84 occupies the largeportion of the supplementary angle of the effective magnetic poleopening angle θm. Therefore, the bridge 84 is attracted toward the tooth91 and the reluctance torque predicted in reference to FIG. 32 isgenerated.

Further, a situation of generating the reluctance torque by efficientlyinterlinking the excitation magnetic flux of the tooth 91 with thebridge 84 as described above, is continued from a timing shown in FIG.37A to a timing shown in FIG. 37B. FIG. 37A shows a state immediatelyafter starting to align the bridge 84 to the tooth 91. FIG. 37B shows astate in which one of the bridge 84 and the tooth 91 is incorporated inother range by rotating the rotor 80 from the state of FIG. 37A. Asshown by FIG. 38, the reluctance torque is generated between the timingsand is substantially constant therebetween. Further, since thereluctance torque is generated by such timings, the magnet torque andthe reluctance torque are connected without gap in view of a verticalrow.

It is known from FIG. 36 that an optimum value of the advancing phaseangle θf is a half of the bridge opening angle θr in electric angle.However, since the tooth 91 is provided with an opening angle to somedegree, a substantially the same effect is achieved even when theadvancing phase angle θf is shifted within the range. FIG. 39 shows asituation of increasing the phase angle θf at maximum in the range. FIG.40 conversely shows a situation in which the advancing phase angle θf isminimized in the range. Therefore, a range of a value to be taken by theadvancing phase angle θf is a range constituting a center by ½ of thebridge opening angle θr in electric angle and constituting a widththereof by an opening angle in electric angle of a width of the tooth atan excitation center of the reluctance torque. When excitation of thereluctance torque is carried out with respect to the single tooth 91,the width is an opening angle in electric angle of the tooth 91. When aplurality of the continuous teeth 91 are excited for the reluctancetorque, the width is an opening angle in electric angle of a widthoccupied by the plurality of teeth 21 and openings there among. Further,in the case of a shape of the tooth in which the magnetic flux iswidened at portions of tips at a front end thereof as shown by FIG. 36and the like, the opening angle of the tooth 91 is constituted by anopening angle including also the portions of the tips. However, in thecase of a shape of the tooth in which the magnetic flux is difficult towiden at portions of tips at a front end thereof as shown by FIG. 41,the width is constituted by an opening angle which does not include theportions of the tips. When excitation is carried out over a plurality ofthe teeth having such a tip shape, the width is constituted by anopening angle excluding tips at both ends on the outermost sides.

An explanation will be given how the above-described will be in the caseof a structure in which a large portion of the supplementary angle ofthe effective magnetic pole opening angle θm is constituted by an airgap (refer to FIG. 42) for comparison. In this case, even whenexcitation current is applied with the above-described advance angle,the reluctance torque is not generated as predicted in FIG. 32. Becausethe excitation magnetic flux of the tooth 91 is difficult to beinterlinked with the bridge 84 since the tooth 91 and the bridge 84 arenot so much proximate to each other at a time point of startingexcitation. The same goes with the case in which the effective magneticpole opening angle θm is extremely proximate to 180° (electric angle) asshown by FIG. 47. It is known from the fact that in order to actuallygenerate the reluctance torque as predicted in FIG. 32, it is necessarythat the effective magnetic pole opening angle θm is not so muchproximate to 180° (electric angle) and the large portion of thesupplementary angle is occupied by the bridge 84.

The higher the rate for occupying the supplementary angle of theeffective magnetic pole opening angle θm by the bridge 84, the better.Because the higher the rate, the more efficiently the excitationmagnetic flux of the tooth 91 is interlinked with the bridge 84.Further, actually, the rate needs to be equal to or larger than 83.3%.The reason resides in whether pulsation of the torque can be reduced incomparison with the case of a motor rotated only by the magnet torque.That is, a torque of the motor rotated only by the magnet torque is asshown by FIG. 43 by taking an example of the case of normal three-phasedriving. That is, the highest portion of the magnet torque of respectivephase is the actual torque. An electric angle between a valley and aridge of the torque is 30°. Therefore, the rate of a torque at thevalley to the maximum torque is given by sin(90°−30°) and is 86.7% inpercentage. In the case of only the magnet torque, the motor torque isprovided with pulsation in this way. It is meaningless when thereluctance torque cannot reduce such a pulsation.

Hence, an investigation will be given of a condition for the reluctancetorque to satisfy such a condition. The reluctance torque is increasedand reduced at a frequency twice as much as that of the magnetic torqueand is provided with peaks on both sides of a peak of the magnet torque.The reluctance torque must achieve a continuity with the magnet torqueby preventing the reluctance torque from becoming smaller than 86.7%,mentioned above, relative to a torque peak having a desired magnitude.For that purpose, it is necessary that the following inequality isestablished with regard to an electric angle θ generated by thereluctance torque.sin(90°±2θ)≧0.867However, both of the magnetic torque and the reluctance torque of therespective phase are constituted by a sine wave form and the peak of thereluctance torque is assumed to be 90°. In this case, attention is givenonly to an advancing angle and therefore, substantially,sin(90°−2θ)≧0.867.Such a relationship between the magnetic torque and the reluctancetorque is shown by FIG. 44. It is known in reference to FIG. 44 that θestablishing the above equation is as shown below.θ≦15°

When the bridge 84 occupies all of the supplementary angle of theeffective magnetic pole opening angle θm, when a central position ofexcitation of the stator 90 (central portion of the tooth 91 when onlythe single tooth 91 is excited) and an end of the effective magneticpole opening angle θm are aligned (in this case, the central position ofexcitation of the stator 90 and an end of the bridge 84 are alsoaligned), the maximum reluctance torque is achieved. The statecorresponds to the peak of the reluctance torque in FIG. 44. A reductionin the rate of occupying the supplementary angle of the effectivemagnetic pole opening angle θm by the bridge 84, corresponds to that thepeak position of the reluctance torque is moved to the left in FIG. 44.Then, when θ is equal to or smaller than 15°, the reluctance torque isequal to or larger than 86.7% of the magnetic torque. In such a range,the reluctance torque serves to reduce pulsation of torque. Therefore,the rate of occupying the supplementary angle of the effective magneticpole opening angle θm by the bridge 84 is requested to be equal to orlarger than 83.3% since(90°−15°)/90°=0.833.

Next, an explanation will be given of a modified example. A modifiedexample shown in FIG. 45 is an example of using a magnet in an inverselybent shape. In this case, a considerable amount of the magnetic memberis present between the magnet and the outer periphery. However, themagnetic flux related to the reluctance torque is not so much influencedby the magnetic member at the portion and therefore, the invention isapplicable thereto. A modified example shown in FIG. 46 is an example ofusing a magnet in a substantially circular arc shape. In this case, onlya small amount of the magnetic member is present between the magnet andthe outer periphery. Naturally, also in this case, almost all of themagnetic flux related to the reluctance torque passes the portion of thebridge and therefore, the invention is applicable thereto.

As has been explained in details, according to the brushless DC motor ofthe embodiment, the effective magnetic pole opening angle θm of themagnet 81 in the rotor 80 is made to be smaller than 180° (electricangle) and is set to fall in a range from 127° (electric angle) to 173°(electric angle). Further, a large portion of the supplementary angle ofthe effective magnetic pole opening angle θm is occupied by the bridge84 of the magnetic member. Therefore, the magnetic flux is easy to beinterlinked with the bridge 84 from the tooth 91 and the reluctancetorque can effectively be utilized. Particularly, rather strongersynthesized torque can be provided by a less amount of using the magnetin comparison with the motor in which the effective magnetic poleopening angle θm is made to be proximate to be almost 180° (electricangle).

Further, when the effective magnetic pole opening angle θm is made to beequal to or smaller than 150° even in such a range, the same synthesizedtorque can be achieved by a further smaller amount of using the magnetin comparison with the case in which the effective magnetic pole openingangle θm is made to be equal to or larger than 150°. Therefore, a largereffect is achieved in view of fabrication cost of the brushless DCmotor. Meanwhile, when the effective magnetic pole opening angle θm ismade to be equal to or larger than 150° in such a range, powerconsumption is made to be small in comparison with a case of making theeffective magnetic pole opening angle θm equal to or smaller than 150°.Therefore, this is more advantageous in view of running cost.

Further, separate magnetic paths at a vicinity of the air gap areconstituted by the magnetic flux related to the magnet torque and themagnetic flux related to the reluctance torque. Therefore, the magneticmember of the rotor 80 is provided with a low possibility of fallinginto magnetic saturation, which is excellent in energy efficiency. Thisalso signifies that uniformity of the magnetic flux distribution at theair gap is excellent. Therefore, the motor is excellent also in view ofmotor properties, vibration and noise. Further, in driving the motor,the magnet torque and the reluctance torque are connected without gap inview of a vertical row. Therefore, pulsation of the synthesized torqueis small.

Further, according to the brushless DC motor of the embodiment, bydriving the motor by excitation current having an advancing phase angleof a half of the opening angle in electric angle of the bridge 84, thereluctance torque can be utilized particularly effectively. Therefore,the effective magnetic pole opening angle θm may be set in theabove-described range, the opening angle of the bridge 84 may be set inconformity with the effective magnetic pole opening angle θm and theopening angle of the bridge 84 may be set as proximate to thecomplementary angle of the effective magnetic pole opening angle θm aspossible. In this case, there may be set a rule of providing theadvancing phase angle of the half of the opening angle in electric angleof the bridge 84 to the excitation current. When the rule is followed,even any of the brushless DC motor in which the effective magnetic poleopening angle θm or the opening angle of the bridge 84 are set asdescribed above, can be driven to generate the reluctance torqueefficiently.

Further, the embodiment is merely an exemplification and does not limitthe invention at all. Therefore, the invention can naturally be improvedor modified variously within a range not deviated from a gist thereof.For example, the pole pair number of the rotor and the shape of themagnet, the number of the teeth of the stator and the like are notlimited to those exemplified. Further, although according to theembodiment, there is shown the motor of the type in which the rotor isdisposed at inside of the stator, the invention is applicable also to amotor of a style in which a rotor is disposed on an outer side of thestator.

As is apparent from the above-described explanation, according to theinvention, there is provided the brushless DC motor capable of achievingnecessary torque even when the magnets are not so much used andalleviating the problem of magnetic saturation and the problem ofnonuniformity of the magnetic flux density. Further, there is provided adriving method capable of driving the brushless DC motor according tothe invention efficiently by the unified rule. Further, the brushless DCmotor and the method of driving the same according to the invention,particularly achieves a significant advantage when used in a motor fordriving an electric power steering apparatus, a capstan or the like.

1. A brushless DC motor comprising: a rotor comprising a magnet; and astator arranged with a plurality of slots at equal pitches in acircumferential direction; wherein a width in a diameter direction of arib portion of the rotor does not exceed a value given by the followingEquation: $\sqrt{\frac{R \times {Wm}}{{Bz}/{Bm}}} \times {Lr}$ where, R:a rate of a leakage magnetic flux at a rib portion to a magnetic fluxprogressing from the magnet to the stator Wm: an effective magnetic polewidth in circumferential direction Bz: a saturation magnetic fluxdensity of a magnetic member of the rotor Bm: a magnetic flux density ofthe rib portion of the rotor in a radial direction of the rotor Lr: alength in the circumferential direction of the rib portion.
 2. Thebrushless DC motor according to claim 1, wherein a contribution of amagnet torque to a total torque is larger than a contribution of areluctance torque to the total torque.
 3. The brushless DC motoraccording to claim 1, wherein a value of Bz/Bm falls in a range of 1.8through 4.4.
 4. The motor of claim 1, wherein the magnet is offset fromthe center of a magnet attaching hole in a circumferential direction. 5.The motor of claim 4, wherein the boundary of the effective magneticpole width is determined by the center in the circumferential directionof the magnet attaching hole.
 6. The motor of claim 1, wherein saidmagnet is arced.
 7. The motor of claim 1, wherein said magnet is linear.8. The motor of claim 7, wherein the width in the diameter direction ofthe rip portion is defined by a portion of a magnetic member of a magnetattaching hole having a least width.
 9. A brushless DC motor comprising:a rotor having a magnet; and a stator comprising a plurality of slots atequal pitches in a circumferential direction; wherein a width in adiameter direction of a rib portion of the rotor does not exceed a valuegiven by the following Equation:$\frac{Q \times {Wb}}{{Bz}/{Bb}} \times \frac{( {{Lr} + {Wm}} )}{Lb}$where, Q: a rate of a leakage magnetic flux at the rib portion to amagnetic flux passing from a tooth of the stator to a bridge of therotor Wb: a width in a circumferential direction of the bridge of therotor Wm: an effective magnetic pole width in circumferential directionBz: a saturation magnetic flux density of a magnetic member of the rotorBb: a magnetic flux density of a bridge of the rotor in driving themotor Lr: a length in the circumferential direction of the rib portionLb: a length in a diameter direction of the bridge.
 10. The brushless DCmotor according to claim 9, wherein a contribution of a magnet torque toa total torque is larger than a contribution of a reluctance torque tothe total torque.
 11. The brushless DC motor according to claim 9,wherein a value of Bz/Bb falls in a range of 1.8 through 4.4.
 12. Astructure of a brushless DC motor comprising: a rotor comprising amagnet; and a stator arranged with a plurality of slots at equal pitchesin a circumferential direction; wherein a width in a diameter directionof a rib portion of the rotor does not exceed a smaller one of a valuegiven by the following Equation 1:$\sqrt{\frac{R \times {Wm}}{{Bz}/{Bm}} \times {Lx}}$ and a value givenby the following Equation 2:$\frac{Q \times {Wb}}{{Bz}/{Bb}} \times \frac{( {{Lr} + {Wm}} )}{Lb}$where, R: a rate of a leakage magnetic flux at a rib portion to amagnetic flux progressing from the magnet to the stator Q: a rate of aleakage magnetic flux at the rib portion to a magnetic flux passing froma tooth of the stator to a bridge of the rotor Wm: an effective magneticpole width in circumferential direction Bz: a saturation magnetic fluxdensity of a magnetic member of the rotor Bm: a magnetic flux density ofthe rib portion of the rotor in a radial direction of the rotor Bb: amagnetic flux density of a bridge of the rotor in driving the motor Lr:a length in the circumferential direction of the rib portion Wb: a widthin the circumferential direction of the bridge of the rotor Lb: a lengthin a diameter direction of the bridge.
 13. The structure of a brushlessDC motor according to claim 12, wherein at least one of a value Bz/Bmand a value Bz/Bb fall in a range of about 1.8 through about 4.4. 14.The motor of claim 12, wherein the magnet is offset from the center of amagnet attaching hole in a circumferential direction.
 15. The motor ofclaim 14, wherein the boundary of the effective magnetic pole width isdetermined by the center in the circumferential direction of the magnetattaching hole.
 16. The motor of claim 12, wherein said magnet is arced.17. The motor of claim 12, wherein said magnet is linear.
 18. The motorof claim 17, wherein the width in the diameter direction of the ripportion is defined by a portion of a magnetic member of a magnetattaching hole having a least width.